2 Answers
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Rule of Odds states that having an odd number of objects in an image will be more interesting and therefore pleasing. In case there is an even number of objects, your brain would have an easy time "organizing" the objects into pairs and therefore bringing in symmetry and dullness.

If you have one main object, accompany it with two supporting objects, not one. This way, one of them will be a middle one.

We can find a parallel from the art of writing, where rule of three states remember that lists of three examples are the most efficient in carrying forward the presented idea.

Human eye tends to wander to the center of a group. With even number of objects, eye will end up at the negative space in center.

The rule becomes important when trying to achieve a visually pleasing composition of several objects. A common form of usage is having three objects in frame, they always form either a line or a triangle, both are considered pleasurable shapes.

The rule will not matter with larger groups though, few people will feel any different if there are 36 or 37 fish in the sea. The amount translates to "plenty" in brain either way.

You should strive to apply the rule when including a "group of" objects as an important element of your photo. E.g. five flowers in a vase will be more pleasing than four or six.

Implied from the rule is that you should have an even number of objects if the paired relationship or dullness is what you want to express (for example, a shot of students sitting in pairs would carry the idea of a dull long lesson, while adding a teacher would turn it around into a photo of educational interaction).

By the way, both the question and this answer serve as examples of using Rule of Odds.

@Matt Grum, would you agree that couple photography works well if the persons are intimately touching each other so they almost form a single subject (the couple), but has an awkward feel when the partners are apart?
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ImreMay 2 '11 at 17:01

Hmm, I would say that actually your last line should have been a numbered line, hence invalidating that point... :-)
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Kendall Helmstetter GelnerMay 3 '11 at 5:05

Jay almost certainly knows the answer to this question, but has asked it anyway ("seeded it") for the benefit of the site. By asking the question, he made me (and certainly some others) aware of this concept.
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Evan KrallMay 1 '11 at 20:09

And what in hell justifies the downvotes here (4 d.v. at this time)??? @foosion did answer the question correctly. He just wondered how come the referred text does not explain it. From his rank (113) it is evident that he is relatively new at this site, and probably not so familiar with @Jay and his method of "seeding".
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ysapMay 2 '11 at 20:06

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@ysap I downvoted because of what I see as a dig at Jay and his question, like "Why would you ask that? It's a stupid question -- you should've just read the book." I'm fine with removing the downvote and even converting to an upvote if he improves his question.
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Evan KrallMay 3 '11 at 2:05

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Also, it doesn't answer the interesting/important parts of the question.
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mattdmMay 11 '11 at 16:13